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Perfect discrete Morse functions on 2-complexes

 

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Opened Access Perfect discrete Morse functions on 2-complexes
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Author: Ayala Gómez, Rafael
Fernández Ternero, Desamparados
Vilches Alarcón, José Antonio
Department: Universidad de Sevilla. Departamento de Geometría y Topología
Date: 2010
Published in: Image-A : Applicable Mathematics in Image Engineering, 1 (1), 19-26
Document type: Article
Abstract: This paper is focused on the study of perfect discrete Morse functions on a 2-simplicial complex. These are those discrete Morse functions such that the number of critical i-simplices coincides with the i-th Betti number of the complex. In particular, we establish conditions under which a 2-complex admits a perfect discrete Morse function and conversely, we get topological properties of a 2-complex admitting such kind of functions. This approach is more general than the known results in the literature [7], since our study is not restricted to surfaces. These results can be considered as a first step in the study of perfect discrete Morse functions on 3-manifolds.
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URI: http://hdl.handle.net/11441/26183

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